APPLICATION OF CONVENTIONAL TECHNIQUES At 
Design step 2.1. Make a polar plot of H(jw)G(jw). 
Design step 2.2. Approximate the sampled loop transfer function 
= » H(jw + jnwo)G(jw + jnwo) by a vector addition of a few sideband 
terms to the fundamental plot obtained in step 2.1. 
Design step 2.3. Select a network transfer function N(jw) by conven- 
tional methods, using such aids as M circles if desired, and replot the 
compensated loop transfer function 
= >» N (jes + jneso)G(jo + jroo) H (jw + jneoo) 
using again only a few terms in the expansion. 
Design step 2.4. After repeated application of step 2.3 indicates a 
probably satisfactory design, check the performance by conventional 
z-transform techniques or by experimentation. Repeat the last two steps 
until the specifications are met. 
The accuracy as well as the difficulty of application of this method, 
which was first proposed in detail by Linvill,?*° increases with the 
number of terms included in the approximation to (6.3). The principal 
virtue of the method lies in its immediate use of well-known design tech- 
niques with a modification of the plots to include what might be called the 
“first-order”’ effects of sampling. 
A rough check on the accuracy of the method is possible by comparing 
ie} 
> G(jw + jnwo)H (jw + jnwo) with the exact 
plot obtained with z-transform methods. A specific example is used for 
illustration later in this chapter. 
Method 3. Introduction of a sampling switch between plant and 
network. 
2 
the approximate plot of i 
Design step 3.1. Approximate the continuous connection between the 
network and the plant by a fictitious sampler and hold (see Fig. 6.3). 
Design step 3.2. Design for the pulse transform of the shaping network 
N(z), using either frequency- or time-domain (Chap. 7) methods. 
Design step 3.3. Obtain the continuous transfer function N(s) which 
corresponds to N(z). 
Design step 3.4. Check the design with exact analysis techniques. 
This method, which was originally proposed by Sklansky,** aims to use 
